If you use a surrogate key, you still need a unique constraint in the table (probably the same columns you would otherwise call your natural PK). If your unique constraint isn't sufficient to capture the difference you mention, you need to add more columns.
However, that's strictly better than the natural PK situation, where you would need to not only add new columns to the key, but also add those columns to all referencing tables.
However, that's strictly better than the natural PK situation, where you would need to not only add new columns to the key, but also add those columns to all referencing tables.